#include<iostream>#include<cstdio>#include<cmath>using namespace std;const double eps = 1e-8;inline int sgn(double a){ return (a > eps) - (a < -eps); }struct point { double x, y; point(double _x = 0, double _y = 0): x(_x), y(_y) { } void input() { scanf("%lf%lf", &x, &y); } double len() const { return sqrt(x * x + y * y); } point trunc(double l) const { double r = l / len(); return point(x * r, y * r); } point rotate_left() const { return point(-y, x); } point rotate_right() const { return point(y, -x); }}p[100000];point operator+(const point& p1, const point& p2) { return point(p1.x + p2.x, p1.y + p2.y);}point operator-(const point& p1, const point& p2) { return point(p1.x - p2.x, p1.y - p2.y);}double operator^(const point& p1, const point& p2) { return p1.x * p2.x + p1.y * p2.y;}double operator*(const point& p1, const point& p2) { return p1.x * p2.y - p1.y * p2.x;}struct circle { point c; double r; circle() { } circle(const point& _c, double _r): c(_c), r(_r) { } void input() { c.input(); scanf("%lf", &r); }}cir[105],c[105];double dist(point a,point b){ return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}bool get_intersection(const circle& cir1, const circle& cir2, point& c1, point& c2) { double d = (cir1.c - cir2.c).len(); if (sgn(d - (cir1.r + cir2.r)) > 0 || sgn(d - fabs(cir1.r - cir2.r)) < 0) return false; double p = (d + cir1.r + cir2.r) / 2.0; double h = sqrt(fabs(p * (p - d) * (p - cir1.r) * (p - cir2.r))) * 2.0 / d; point pp = cir1.c + (cir2.c - cir1.c).trunc(sqrt(fabs(cir1.r * cir1.r - h * h))); c1 = pp + (cir2.c - cir1.c).rotate_right().trunc(h); c2 = pp - (cir2.c - cir1.c).rotate_right().trunc(h); return true;}int main(){ int n,s,i,j; double r; while(scanf("%lf %d",&r,&n)!=EOF) { for(i=1;i<=n;i++) scanf("%lf %lf %lf",&cir[i].c.x,&cir[i].c.y,&cir[i].r); int t=0,ret=0; for(i=1;i<=n;i++) { if(sgn(cir[i].r-r)>0)continue; c[t].c.x=cir[i].c.x; c[t].c.y=cir[i].c.y; c[t].r=r-cir[i].r; p[t]=c[t].c; t++; } point a,b; ret=s=t; for(i=0;i<s;i++) for(j=i+1;j<s;j++) { bool k=get_intersection(c[i],c[j],a,b); if(k) { p[ret++]=a; p[ret++]=b; } } int ans=0,m; for(i=0;i<ret;i++) { m=0; for(j=0;j<s;j++) { if(sgn(dist(p[i],c[j].c)-(c[j].r))<=0) m++; } if(m>ans)ans=m; } printf("%dn",ans); } return 0;}
